Trivial Witt groups of flag varieties

Baptiste Calmès (1) , Jean Fasel

1 LML - Laboratoire de Mathématiques de Lens

Let G be a split semi-simple linear algebraic group over a field, let P be a parabolic subgroup and let L be a line bundle on the projective homogeneous variety G/P. We give a simple condition on the class of L in Pic(G/P)/2 in terms of Dynkin diagrams implying that the Witt groups W^i(G/P,L) are zero for all integers i. In particular, if B is a Borel subgroup, then W^i(G/B,L) is zero unless L is trivial in Pic(G/B)/2.

Domaines: Géométrie algébrique [math.AG]; K-théorie et homologie [math.KT]

Baptiste Calmès, Jean Fasel. Trivial Witt groups of flag varieties. 2011. ⟨hal-00579798⟩